I'm creating a block-based game and am ready to start developing the avatar. I would like to use the Minecraft avatar model but use my own higher resolution texture. Can I do this or will I be breaking some law or setting myself up to be sued?
This is not legal advice because I am not a lawyer, you should consider talking to a real lawyer if you want a proper answer to any law-related topic.
You can't use the assets that ship with Minecraft. You can, however, create your own box-man avatar, and that would probably be a much better idea for a variety of reasons even disregarding the legal or ethical issues involved.
For example, it would be built for your technology instead of somebody else's, you have more control over it and can be more creative, et cetera.
First off, I totally agree with Josh Petrie's answer, you should have your own models. But in this kind of case there is an obvious solution that people seems to forget or doesn't want to consider...
You can ask the owner the right to use its work... explains how you would like to use it, what you need exactly etc... don't be too greedy, but if you don't ask you won't get anything.
On the following page about the Minecraft author http://www.mojang.com/notch/,you can find notch email : firstname.lastname@example.org
He/They will probably answer you "NO", but nothing ventured, nothing gained.